I don't think you've considered all the weaknesses of the system you're suggesting...
Hillary Clinton won 300 counties while Trump won 5000.
Suppose right before the election Dr. Evil gerrymandered the whole country so there are only 3 counties - two in his house, and one for everyone else. Based on your reckoning he is the rightful president because he won the two counties in his house.
If you think that the election of a nation should be swayed by a handful of cities
I would argue the election would be swayed by vast numbers of individual voters whose votes are weighted equally regardless of race, religion, gender, (etc...), and where they live.
The weighting based on where you live can easily be leveraged into weighting based on income level, race, or religion. For example suppose we don't like the Mormons - well if you're from Utah your vote now counts 1/10 as much as everyone else's. This negatively influences of perceived fairness of the government which is directly related to its perceived legitimacy. A government perceived as illegitimate will be eventually be forced to govern by violence, which is in no one's best interest.
You seem to be OK with weighting different peoples votes differently. I'd be interested to hear at what point you consider the weights to be too extreme? My understanding is the current system results in maximum of about a 1:4 disparity between Californians versus Wyomingites (Wyomines?) (https://youtu.be/7wC42HgLA4k?t=1m43s). 1/10? 1/100?
How do you justify the particular weighting you've selected as optimal as oppose to any other?